Mathematicians create a tetrahedron that always lands on the same side

image via New Scientist

June 27, 2025, 4:47 PM

• •Mathematicians built a real-life version of a self-righting tetrahedron, named the Bille, using carbon fiber and tungsten, decades after it was theorized.
• •The shape, discovered with the help of powerful computers, always rests on the same side due to uneven weight distribution.
• •The project, led by Gábor Domokos, involved extensive engineering to achieve the necessary density difference for the shape to function.
• •Domokos hopes this work could influence engineering, such as designing more stable lunar landers.

Researchers have successfully built a monostable tetrahedron, a four-sided shape that always rests on the same side, a concept proposed decades ago. This achievement, realized through extensive computational searches and precise engineering, involved creating a shape with an uneven mass distribution using carbon fiber and tungsten. The team, led by Gábor Domokos, spent considerable effort and resources to overcome the challenges in creating a real-world example of the theoretical shape. Domokos believes this research has implications for improving the stability of objects, such as lunar landers.

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